The present invention generally relates to imaging technology. More particularly, the present invention relates to computing geometric wavelets representation based on active contours.
Imaging systems have been developed for a variety of purposes. Some of these are for computer graphics, for video encoding for transferring video files, and for generating computer-enhanced pictures/videos. For example, an imaging system may rely upon an edge detection method for video data compression. Edge detection may also allow generating pictures and/or videos that will allow shape analysis. For example, there are a number of numerical algorithms for computing a near-minimizer of one of the methods of edge detection, Mumford-Shah functional. However, they do not produce an actual segmentation of the image into distinct regions with disjoint interiors. Instead, they classify pixels with an “edge” score, where the score implies the probability that the pixel is an edge pixel. This method may make difficult extraction of true segmentation from this “fuzzy” classification. For example, some computer aided diagnostic procedures for the medical field require that an actual segmentation curve be computed so that shape analysis can be applied to the segmented object for the purpose of detecting abnormalities.
In the medical field, an imaging system that can provide as much detail as possible from a limited video data may be valuable to a radiologist in his work since the radiologist relies on X-ray pictures, MRI or CAT scans, and other visual rendition of a patient's body in assessing a patient's health. However, in some situations, there may not be enough data available for generation of an acceptable video/picture output. For example, in photon-limited images, the random nature of photon emission and detection is the dominant source of noise in the imaging system. In these cases, the relatively small number of detected photons is a factor limiting the signal-to-noise ratio. These applications comprise Positron Emission Tomography (PET), Single Photon Emission Computed Tomography (SPECT), Confocal Microscopy, and Infrared (IR) imaging.
The data collected by these imaging systems are usually assumed to obey a spatial Poisson distribution involving a two-dimensional intensity image that descries the probability of photon emissions at different locations in space. The mean and variance of a Poisson process are equal to the intensity, where the intensity mean corresponds to the “signal” of interest and the variability of the data about the mean can be interpreted as “noise.” In some sense, it may be said that the noise in photon-limited imaging is signal dependent. Thus, a reconstruction method that removes the Poisson noise while preserving the main feature of the image will be useful.